Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) are often used to implement a variety of analog functions and digital logic. For instance, MOSFETs can be arranged to form of large scale integrated circuits (LSI) and very large scale integrated circuits (VLSI). A MOSFET can be controlled to provide an output that varies as a function of one or more operating parameters. The drain current (ID) through a given MOSFET device can be expressed as follows:
      I    D    =            (              W        L            )        ⁢          1      2        ⁢    μ    ⁢                  ⁢                            C          OX                ⁡                  (                                    V              GS                        -                          V              T                                )                    2      
where:                W=channel width of the MOSFET;        L=channel length of the MOSFET;        COX=capacitance per unit area of the gate-to-channel capacitor for which the oxide layer serves as a dielectric; and        VGS=gate-to-source voltage of the MOSFET.        
Of particular interest from the foregoing equation is the threshold voltage (VT). VT corresponds to a voltage applied to the gate of a field effect transistor (FET) that is necessary to open a conductive channel between the source and drain. More specifically, for the case of a MOSFET, VT is the minimum voltage at the gate that is necessary for an inversion layer to be formed at the semiconductor surface so that significant current flows through the device. For many integrated N-channel MOSFET devices, VT is in the range of about 0.3 to 1.5 V.
Various approaches have been developed to determine or extract VT for a MOSFET. One approach to extract VT is to obtain VT from a single voltage measurement. The efficacy of this method generally depends on the selected current, as different drain currents tend to result in different threshold voltages. Another approach is a linear extrapolation method in which a maximum transconductance is employed to locate a point of maximum slope along a plot of drain current versus gate-source voltage. However, the transconductance is dependent on the series resistance of the MOSFET, which can introduce errors. Other approaches to derive an indication of VT include a ratio method and a quasi-constant-current method, which have various limitations in addition to their complexities.
The extracted VT can be utilized for a variety of purposes where it is desirable to reduce process-dependent parameters associated with a MOSFET. Examples for using an extracted value of VT include process monitoring, device characterization, temperature sensing, and voltage reference generation.